Abstract
Abstract In this paper, we define the modular space Z σ ( s , p ) by using the Zweier operator and a modular. Then, we consider it equipped with the Luxemburg norm and also examine the uniform Opial property and property β. Finally, we show that this space has the fixed point property. MSC:40A05, 46A45, 46B20.
Highlights
In literature, there are many papers about the geometrical properties of different sequence spaces such as [ – ]
The Opial property is important because Banach spaces with this property have the weak fixed point property
We say that X has the uniform Opial property if for any ε > there exists r > such that for any x ∈ X with x ≥ ε and any weakly null sequence {xn} in the unit sphere of X, the inequality + r ≤ limn→∞ inf xn + x holds
Summary
There are many papers about the geometrical properties of different sequence spaces such as [ – ]. The Opial property is important because Banach spaces with this property have the weak fixed point property. A Banach space X has the Opial property if for any weakly null sequence {xn} in X and any x in X \ { }, the inequality limn→∞ inf x < limn→∞ inf xn + x holds.
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